Auto merge of #54609 - kzys:404-search, r=GuillaumeGomez
Auto merge of #54609 - kzys:404-search, r=GuillaumeGomez

Add the library search box on the 404 page

It actually has a link to search already, but it would be better to
have the search "box" as like index.md to be consistent.

<style> can be shared with index.md, but these pages currently
use https://doc.rust-lang.org/rust.css directly.

Fixes #14572.

GBGamer/rust,GBGamer/rust,GBGamer/rust,graydon/rust,graydon/rust,GBGamer/rust,aidancully/rust,aidancully/rust,GBGamer/rust,GBGamer/rust,graydon/rust,aidancully/rust,GBGamer/rust,graydon/rust,graydon/rust,graydon/rust,GBGamer/rust,aidancully/rust,aidancully/rust,aidancully/rust